image segmentation dr. abdul basit siddiqui. contents today we will continue to look at the problem...

Image SegmentationImage Segmentation

Dr. Abdul Basit Siddiqui

Contents

• Today we will continue to look at the problem of segmentation, this time though in terms of thresholding

• In particular we will look at:– What is thresholding?– Simple thresholding– Adaptive thresholding

Segmentation

• Divide the image into segments.

• Each segment:– Looks uniform– Belongs to a single object.– Have some uniform attributes.– All the pixel related to it are connected.– …

Detection of Discontinuities

• Point Detection

• Line Detection

• Edge Detection

Detection of DiscontinuitiesDetection of Discontinuities

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mask 3x3n with Convolutio

Matrix notation

w = [w1 w2 ... wn] maske

Z = [ z1 z2 … zn] tilhørende billed pixels

R(x,y) = [w] [Z]’

Point detectionPoint detection

TR

T is a non-zero threshold

Segmentation Algorithms

• Segmentation algorithms are based on one of two basic properties of intensity values discontinuity and similarity.

• First category is to partition an image based on abrupt changes in intensity, such as edges in an image.

• Second category are based on partitioning an image into regions that are similar according to a predefined criteria. Thresholding, Histogram Thresholding approach falls under this category.

Thresholding

• Thresholding is usually the first step in any segmentation approach

• We have talked about simple single value thresholding already

• Single value thresholding can be given mathematically as follows:

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),( 1),(

Thresholding

3 5 7 3 4 2 1

2 4 9 10 22 9 3

3 5 12 11 15 10 3

5 6 11 9 17 19 1

2 3 11 12 18 16 2

3 6 8 10 18 9 5

4 6 7 8 3 3 1

Thresholding

3 5 7 3 4 2 1

2 4 9 10 22 9 3

3 5 12 11 15 10 3

5 6 11 9 17 19 1

2 3 11 12 18 16 2

3 6 8 10 18 9 5

4 6 7 8 3 3 1

Thresholding

3 5 7 3 4 2 1

2 4 9 10 22 9 3

3 5 12 11 15 10 3

5 6 11 9 17 19 1

2 3 11 12 18 16 2

3 6 8 10 18 9 5

4 6 7 8 3 3 1

Thresholding

3 5 7 3 4 2 1

2 4 9 10 22 9 3

3 5 12 11 15 10 3

5 6 11 9 17 19 1

2 3 11 12 18 16 2

3 6 8 10 18 9 5

4 6 7 8 3 3 1

Thresholding Example

• Imagine a poker playing robot that needs to visually interpret the cards in its hand

Original Image Thresholded Image

But Be Careful

• If you get the threshold wrong the results can be disastrous

Threshold Too Low Threshold Too High

Basic Global Thresholding

• Based on the histogram of an image

• Partition the image histogram using a single global threshold

• The success of this technique very strongly depends on how well the histogram can be partitioned

Basic Global Thresholding Algorithm

• The basic global threshold, T, is calculated as follows:1. Select an initial estimate for T (typically the average

grey level in the image)

2. Segment the image using T to produce two groups of pixels: G1 consisting of pixels with grey levels >T and G2 consisting pixels with grey levels ≤ T

3. Compute the average grey levels of pixels in G1 to give μ1 and G2 to give μ2

Basic Global Thresholding Algorithm

4. Compute a new threshold value:

5. Repeat steps 2 – 4 until the difference in T in successive iterations is less than a predefined limit T∞

•This algorithm works very well for finding thresholds when the histogram is suitable

221

T

Thresholding Example 1

Thresholding Example 2

Problems With Single Value Thresholding

• Single value thresholding only works for bimodal histograms

• Images with other kinds of histograms need more than a single threshold

Problems With Single Value Thresholding (cont…)

• Let’s say we want to isolate the contents of the bottles

• Think about what the histogram for this image would look like

• What would happen if we used a single threshold value?

Single Value Thresholding and Illumination

• Uneven illumination can really upset a single valued thresholding scheme

Basic Adaptive Thresholding

• An approach to handling situations in which single value thresholding will not work is to divide an image into sub images and threshold these individually

• Since the threshold for each pixel depends on its location within an image this technique is said to adaptive

Basic Adaptive Thresholding Example

• The image below shows an example of using adaptive thresholding with the image shown previously

• As can be seen success is mixed

• But, we can further subdivide the troublesome sub images for more success

Basic Adaptive Thresholding Example (cont…)

• These images show the troublesome parts of the previous problem further subdivided

• After this sub division successful thresholding can be achieved

Segmentation Based on Clustering